Highest Common Factor of 315, 523, 178 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 315, 523, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 315, 523, 178 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 315, 523, 178 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 315, 523, 178 is 1.

HCF(315, 523, 178) = 1

HCF of 315, 523, 178 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 315, 523, 178 is 1.

Highest Common Factor of 315,523,178 using Euclid's algorithm

Highest Common Factor of 315,523,178 is 1

Step 1: Since 523 > 315, we apply the division lemma to 523 and 315, to get

523 = 315 x 1 + 208

Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 208 and 315, to get

315 = 208 x 1 + 107

Step 3: We consider the new divisor 208 and the new remainder 107, and apply the division lemma to get

208 = 107 x 1 + 101

We consider the new divisor 107 and the new remainder 101,and apply the division lemma to get

107 = 101 x 1 + 6

We consider the new divisor 101 and the new remainder 6,and apply the division lemma to get

101 = 6 x 16 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 315 and 523 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(101,6) = HCF(107,101) = HCF(208,107) = HCF(315,208) = HCF(523,315) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 178 > 1, we apply the division lemma to 178 and 1, to get

178 = 1 x 178 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 178 is 1

Notice that 1 = HCF(178,1) .

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Frequently Asked Questions on HCF of 315, 523, 178 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 315, 523, 178?

Answer: HCF of 315, 523, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 315, 523, 178 using Euclid's Algorithm?

Answer: For arbitrary numbers 315, 523, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.